Problem
Convert 130 kg to lbs. Use dimensional analysis (unit cancellation) and report a rounded value suitable for general chemistry measurement work.
Conversion principle (dimensional analysis)
A unit conversion is performed by multiplying by a conversion factor written as a ratio so that units cancel, leaving the desired unit.
Exact definition: \[ 1\ \text{lb} = 0.45359237\ \text{kg} \]
Step-by-step: 130 kg to pounds
Step 1: Build a factor that cancels kilograms.
Invert the definition to obtain pounds per kilogram: \[ \frac{1\ \text{lb}}{0.45359237\ \text{kg}} \]
Step 2: Multiply and cancel units.
\[ 130\ \text{kg}\cdot \frac{1\ \text{lb}}{0.45359237\ \text{kg}} = \frac{130}{0.45359237}\ \text{lb} = 286.6009408403408549\ \text{lb} \]
Step 3: Round using significant figures.
The written value 130 kg is often ambiguous in significant figures (a trailing zero without a decimal point may or may not be significant). Common reporting choices are shown below.
| Given notation | Implied significant figures | Rounded result (lb) | Typical meaning in measurement |
|---|---|---|---|
| 130 kg | Ambiguous (often treated as 2 or 3) | \(290\ \text{lb}\) (2 s.f.) or \(287\ \text{lb}\) (3 s.f.) | Rounded measurement without explicit decimal precision |
| 130.0 kg | 4 | \(286.6\ \text{lb}\) | Measured to the nearest 0.1 kg |
| 130.00 kg | 5 | \(286.60\ \text{lb}\) | Measured to the nearest 0.01 kg |
Visualization: aligning 130 kg with its pound equivalent
Common pitfalls
- Using the factor in the wrong direction: multiplying by \(\frac{0.45359237\ \text{kg}}{1\ \text{lb}}\) converts lb to kg, not kg to lb.
- Rounding too early: keep extra digits during the division, then round the final value to match measurement precision.
- Mixing mass units in later steps: in chemistry calculations, keep mass units consistent (often grams) after converting.
Final answer
\[ 130\ \text{kg} = 286.6009408403\ \text{lb} \approx 286.6\ \text{lb} \]